Small‐Sample Efficiency and Accuracy of Stress‐Strength Reliability Estimation and Bootstrapped Confidence Intervals for the Discrete Distribution

ABSTRACT Estimation of stress‐strength reliability is an important research topic in engineering and statistics. Traditional methods predominantly rely on simple random sampling to estimate system reliability. However, in recent years, ranked set sampling has emerged as a cost‐effective and efficient alternative to simple random sampling. Despite its growing popularity, the application of ranked set sampling to stress‐strength reliability in discrete models has not been sufficiently explored. This study provides a detailed statistical analysis of stress‐strength reliability when stress and strength are modeled as independent discrete random variables with a Poisson transmuted record type exponential distribution. Both point estimates and bootstrap confidence intervals are used to derive stress‐strength reliability estimates under both simple random sampling and ranked set sampling frameworks. The effectiveness of the estimates is evaluated through extensive Monte Carlo simulations, comparing their performance in various settings. Furthermore, simulation results from the analysis of three datasets demonstrate that the ranked set sampling estimates generally outperform traditional simple random sampling estimates in terms of both efficiency and accuracy. These findings highlight the potential advantages of ranked set sampling for estimating system reliability and contribute significantly to the field by demonstrating the applicability of the method to discrete models. Particularly for small sample sizes, the ranked set sampling method provides more consistent and reliable estimates than simple random sampling, lower confidence intervals, and reduced estimation errors.